The invention relates to a data processing system which executes stored programs in highly parallel fashion. In the prior art, highly parallel execution of stored programs is realized by complex techniques which either divide the program into parts which may be independently executed by separate parts of a data processing system, or the data processing system is arranged to look ahead of the current instruction in a sequential program to determine what other instructions may be performed concurrently with the current instruction. It is an object of this invention to provide a method for realizing highly parallel execution of stored programs by data processing apparatus that identifies instructions available for concurrent execution throughout the program.